1. References
Vedic Mathematics
1) Vedic Mathematics or Sixteen Simple
Mathematical Formulae from the Vedas
(For one-line answers to all mathematical
M. Krishnamoorthy (moorthy)
problems), Motilal Banarsidass Publishers,
email address: moorthy@cs.rpi.edu Delhi, 1965. ISBN 81-208-0164-4
URL: 2) History of Hindu Mathematics - A source
http://www.cs.rpi.edu/~moorthy/vm Book Parts 1&2 B. Datta and A. N. Singh,
Asia Publishing House, Bombay, 1935.
Outline of the Course Summary of Course
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Introduction and Multiplication Sutra Considers the origin of different methods
(chapter 3) 2/2/97 used in Vedic Mathematics
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Practical Applications of Multiplication Learn Sutras to know how to do
and Division Sutra (chapter 4) 2/9/97 calculations in a different (faster/more
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Argumental Division (chapter 1) 2/16/97 efficient manner).
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Recapitulation and More exercises 2/23/97 Usefulness of these methods in a
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Factorization of Simple Quadratics (chapter calculator/computer age.
7) 3/2/97
2. About Students Agenda for Today
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Find out any relevant background and Brief History Vedas, Vedangas and
interest of the audience Upavedas
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What do they understand by vedic Why did the vedic people do mathematics?
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mathematics? Some of the mathematical inventions that
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Why one should do mathematics in the were attributed to India. -
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20th/21st century? Famous Indian mathematicians of the
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Can you name a famous 20th century Indian bygone and their writings
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Mathematician? Sutras for Multiplication and Examples
Overview HISTORY
Let us say that you want to multiply Explain how all the individual topics fit
1) 1257 * 1001 together
2) 777 * 999
3) 113 * 108
3. Period of Vedic Mathematics Other Claims
This is a book by Shankaracharya (1884-
1960) of Puri. It was meant to be the first of Some others claim that this book is about
16 volumes covering aspects of Hindu Mathematics between Aryabhatta
mathematics by explaining the use of 16 and Bhaskara - that is roughly between 500
sutras from the Vedas. All of these volumes and 1100 AD.
were lost. Before he dies, he rewrote Vol. 1 Chandogya Upanishad - Story about Narada
from his memory. This volume covers quick and Sage Sanatkumara.
methods for doing arithmetic.
Vedas, Vedangas and
Upavedas
Upangas
Fourteen-fold Vedic Knowledge: 4 Upavedas (Ayurveda, Gandharvaveda,
1) 4 Vedas (Rg, Yajur, Sama and Atharva) - Dhanurveda and Sthapatyaveda)
originally oral in nature.
2) 6 Vedangas (phonetics, grammar, Vedas refer to a body of knowledge that
etymology, metronomy(chandas), reveals different means and ends available
Astronomy and Astrology, and Kalpa) to the human being.
4) 4 Upavedas (Analysis, Logic, Puranic
Literature) and Darma Sastra
4. Vedic Mathematics Uses of Mathematics
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Most important sources for Vedic Kalpasutras gave directions for conducting
Mathematics are found in Astronomy sacrificial fires at different times of the year.
&Astrology and Kalpa (rules for rituals and So they need to calculate the planetary
ceremonies). positions which needed mathematics. They
Evidence is usually in the form of sutras (a also need to construct calendars/panchangas
peculiar form of writing which is very for lunar as well solar months. Astrology
concise and often uses a poetic style to also needed considerable mathematical
capture the essence of argument or result. calculations.
Sutras Examples
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Condensation of sutras so that minimal Sutra can be thought of Sanskrit equivalent of
writing material is used. This was the form something like: “i” before “e” except after
in which the contents of Brahmanas were “c”.
preserved. This was later used by various Example: Nikhilam Navatashcaramam
philosophical and scientific schools such as Dashatah
statecraft (arthasasastra). A concise Sanskrit All from nine and the last from 10.
statement that gives a rule or principle to be
followed, for example, in grammar, in ritual
or in mathematics
5. Uses of that sutra More Examples
Multiplication
8x 7x 7x9
9 8 9x9
8 -2 7 -3
9 -1 8 -2 12 x 13
-------- --------- 14 x 17
7 2 5 6 19 x 19
Why does it work? Upasutra
(x-a) * (x-b) = x^2 -x(a+b) + ab There is a upasutra (subsutra) of one word
= x(x-a-b) + ab anurupyena which means “Proportionately”.
In 8 x 9 In other words, one can take any base that is
x-a = 8, x-b=9 and x is taken to be 10. suitable.
Before I explain what is meant by base:
91 -9
89 -11
80 99.
6. Base Examples
The base we choose in the previous example
is 100. ( or x in the formula is 100). 56 6 45 -5 211 11
54 4 47 -3 209 09
Bases can be understood from the positional -------- --------- -------------
number system (again this system is 60/2 24 21 15 440 99
believed to be the invention of Indians.
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Normally, numbers are represented in base 10
notation. Computers use binary numbers or
numbers represented in base 2.
Summary Where to get more information
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History of Vedic Mathematics Do more examples.
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Multiplication using sutras Look at the Internet under altavista, search
with vedic-mathematics
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Go to local library/Barnes Nobles/Borders
read a book titled “The Man Who Knew
Infinity”
